The donor pays the gift tax, not the recipient.

However, when making a gift to the USA, there is no gift tax. In fact the IRS used to have a line on the 1040 where a person could donate (gift) money to the government to "reduce the national debt". It hasn't been on there in recent years. Probably no one used it.

But, you are correct, there is no tax due as Qatar donated the 747 to the USA, the government.

But that brings up an interesting question. If a foreign national, or even a government, gifted a substantial amount ($400M) to a US citizen, would the donor have to pay gift tax to the IRS? The IRS has no jurisdiction over people in other countries.